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Abstract
We complement Weinberg's no-go theorem on the cosmological constant problem in quantum gravity by generalizing it to the case of a scale-invariant theory. Our analysis makes use of the effective action and the BRST symmetry in a manifestly covariant quantum gravity instead of the classical Lagrangian density and the $GL(4)$ symmetry in classical gravity. In this sense, our proof is very general since it does not depend on details of quantum gravity and holds true for general gravitational theories which are invariant under diffeomorphisms. As an application of our theorem, we comment on an idea that in the asymptotic safety scenario the functional renormalization flow drives a cosmological constant to zero, solving the cosmological constant problem without reference to fine tuning of parameters. Finally, we also comment on the possibility of extending the Weinberg theorem in quantum gravity to the case where the translational invariance is spontaneously broken.
Highlights
The extremely tiny value of the cosmological constant at the present epoch, around 1ðmeVÞ4, in the history of our Universe poses a very serious problem to the community of both theoretical physics and cosmology [1,2]
In the standard model of particle physics, spontaneous symmetry breaking naturally leads us to expect a cosmological constant of order E4 where E is the energy scale of symmetry breaking
This energy scale ranges from ð100 MeVÞ4 for the QCD deconfinement phase transition to ð1018 GeVÞ4 for symmetry breaking at the Planck scale
Summary
The extremely tiny value of the cosmological constant at the present epoch, around 1ðmeVÞ4, in the history of our Universe poses a very serious problem to the community of both theoretical physics and cosmology [1,2]. It is natural to extend the Weinberg’s no-go theorem, which is a purely classical statement based on field equations, to a quantum mechanical theorem In this respect, note that the cosmological constant problem comes from a clash between particle physics and gravity in the semiclassical approximation where matter fields are quantized while gravity is treated as a classical theory. We wish to generalize the proof to the case where the two field equations are dependent and related via a certain condition [1] The existence of this condition reflects the presence of scale symmetry in a theory, so the generalized Weinberg theorem can be applied to the situation where there is an exact scale symmetry within the framework of quantum gravity.
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